Pith Number

pith:PTA3TBLL

pith:2016:PTA3TBLL5VNNK7PJJ5EQGRFHBB

not attested not anchored not stored refs pending

Vanishing ranges for the mod $p$ cohomology of alternating subgroups of Coxeter groups

Toshiyuki Akita, Ye Liu

arxiv:1604.08277 v1 · 2016-04-28 · math.AT · math.GR · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PTA3TBLL5VNNK7PJJ5EQGRFHBB}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:50:09.699378Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cc1b9856bed5ad57de94f490344a70864048416af8528e08887bec30740eb71

Aliases

arxiv: 1604.08277 · arxiv_version: 1604.08277v1 · doi: 10.48550/arxiv.1604.08277 · pith_short_12: PTA3TBLL5VNN · pith_short_16: PTA3TBLL5VNNK7PJ · pith_short_8: PTA3TBLL

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PTA3TBLL5VNNK7PJJ5EQGRFHBB \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7cc1b9856bed5ad57de94f490344a70864048416af8528e08887bec30740eb71

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb6cc2b966eb1d3b3d97c0ff69bfa90daafcbe1fa859a478d414aba49a102c5b",
    "cross_cats_sorted": [
      "math.GR",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-04-28T00:57:51Z",
    "title_canon_sha256": "7fe54ab560eacee345ce47a38e4596a729443cbb9d8b3218dad25158c7acc0de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.08277",
    "kind": "arxiv",
    "version": 1
  }
}